Computer simulations are one of the most useful tools in modern engineering. To evaluate a proposed solution to a complex engineering problem, an engineer typically uses a Finite Element Analysis (FEA) software tool to construct a mathematical model of the proposed solution and to run FEA simulations based on the mathematical model. For instance, when designing a bridge, a structural engineer can use an FEA tool to construct a model of a proposed design and to run simulations to determine whether any stress “hot spots” exist under various loading conditions.
FEA refers generally to a class of numerical analysis techniques for approximating solutions of partial differential equations. These techniques attempt to break down a complex physical system into simpler subsystems that are analyzed locally. For instance, in the example of the proposed bridge design, a mathematical domain representing the structure of the bridge can be divided into a set of disjoint subdomains each representing a portion of the structure. An unknown function of interest (e.g., displacement or stress) can then be approximated locally over each subdomain.
Several FEA tools are available commercially, such as MSC Nastran by MSC.Software Corporation, COMSOL Multiphysics® by COMSOL AB, SAP 2000® by Computers and Structures, Inc., and ANSYS® by ANSYS, Inc.